\newproblem{lay:4_1_9}{
  % Problem identification
	\begin{large}
	  \hspace{\fill}\newline
    \textbf{Lay, 4.1.9}
	\end{large}
	\\
  \ifthenelse{\boolean{identifyAuthor}}{\textit{Ana Pe\~na Gil, Jan. 19th 2014} \\}{}

  % Problem statement
	Let $H$ be the set of all vectors of the form $\begin{pmatrix}-2t \\ 5t \\ 3t\end{pmatrix}$. Find a vector $\mathbf{v}$ in $\mathbb{R}^3$ such that $H = \mathrm{Span}\{\mathbf{v}\}$. Why does this show that $H$ is a subspace of $\mathbb{R}^3$? \\
}{
   % Solution
	\[\forall\mathbf{v}\in H \Rightarrow \mathbf{v} = \begin{pmatrix}-2t \\ 5t \\ 3t\end{pmatrix} = t \begin{pmatrix}-2 \\ 5 \\ 3\end{pmatrix}\]
	So $H = \mathrm{Span}\{(-2, 5, 3)\}$. Since $H$ is generated by a set of vectors of $\mathbb{R}^3$, by Theorem 4.1, $H$ is a vector subspace of $\mathbb{R}^3$.
}
\useproblem{lay:4_1_9}
\ifthenelse{\boolean{eachProblemInOnePage}}{\newpage}{}
